Assume that the nucleus of the fluorine atom is a sphere with a radius of 5 x 10 ^ -13 cm. Calculate the density of matter in the fluorine nucleus in grams/cm^3. Now convert your answer to tons per cubic centimeter, knowing that there are 454 grams in one pound.
And your trouble with this problem is mainly what?
I don't understand how to set up the conversion problem.. Or what exactly it's asking
The volume of a sphere is (4/3)*pi*r^3. The problem gives radius; substitute and solvge for volume in cc.
The problem doesn't give you the mass of a F nucleus but you know the atomic mass is 19.0 grams for a mol so 1 atom has a mass of 19.0/6.02E23) = ?g
mass = volume x density
Substitute mass and volume from above and solve for density in g/cc.
(grams/454) converts to lbs and (lbs/2000) converts to tons.
You make conversions this way.
Given x factor = new unit
Say you want to convert 500 g to lbs. The factor is 1 lb = 454 g.
500 g x factor = lbs.
500 x (1 lb/454) = 1.1 lbs.
Note that there are two ways to use the factor. One is 1 lb/454 g and the other is 454g/1 lb. How do you know which to use. In this example you want to use 1 lb/454g because this way the grams (the unit we don't want to keep) cancel (g in the numerator cancels with g in the denominator of the factor) and the unit we want to change to (lbs) is left alone.
To calculate the density of matter in the fluorine nucleus, we need to divide the mass by the volume.
Since the nucleus is assumed to be a sphere, we can use the formula for the volume of a sphere:
Volume = (4/3) * pi * (radius)^3
Given that the radius of the fluorine nucleus is 5 x 10^-13 cm, we can substitute it into the formula:
Volume = (4/3) * pi * (5 x 10^-13 cm)^3
Now, let's calculate the volume:
Volume = (4/3) * pi * (125 x 10^-39 cm^3)
= (500/3) * pi * 10^-39 cm^3
Next, we need to know the mass of the fluorine nucleus. The atomic mass of fluorine is approximately 19 atomic mass units (AMU). Each AMU is approximately equal to 1.66054 x 10^-24 grams.
To convert the atomic mass to grams, we multiply by the conversion factor:
Mass = 19 AMU * 1.66054 x 10^-24 grams/AMU
= 3.15403 x 10^-23 grams
Now, we have both the mass and volume, so we can calculate the density:
Density = Mass/Volume
= (3.15403 x 10^-23 grams)/[(500/3) * pi * 10^-39 cm^3]
= (3.15403 x 10^-23 grams)/(1.04719755 x 10^-39 cm^3)
= 3.00924 x 10^16 grams/cm^3
To convert this density to tons per cubic centimeter, we need to know that there are 454 grams in one pound and 2000 pounds in one ton:
Density = 3.00924 x 10^16 grams/cm^3 * (1 pound/454 grams) * (1 ton/2000 pounds)
= 1.66612 x 10^13 tons/cm^3
Therefore, the density of matter in the fluorine nucleus is approximately 3.00924 x 10^16 grams/cm^3 or 1.66612 x 10^13 tons/cm^3.